E228 and E225 in groups,interfaces,modules,plot

Author: fchapoton

src/sage/groups/cubic_braid.py

@@ -805,9 +805,9 @@ def _repr_(self):
             Assion group on 2 strands of type U
         """
         if self._cbg_type == CubicBraidGroup.type.Coxeter:
-            return "Cubic Braid group on %s strands"%(self.strands())
+            return "Cubic Braid group on %s strands" % (self.strands())
         else:
-            return "Assion group on %s strands of type %s"%(self.strands() ,self._cbg_type.value)
+            return "Assion group on %s strands of type %s" % (self.strands() ,self._cbg_type.value)
 
     def index_set(self):
         r"""
@@ -901,7 +901,7 @@ def _internal_test_attached_group(self, attached_group, tester):
         elem = self.an_element()
         att_grp_elem = attached_group(elem)
         if self.is_finite() and self.strands() <= 7: # not realistic for larger number of strands
-            att_grp_elem_back= self(att_grp_elem)
+            att_grp_elem_back = self(att_grp_elem)
             tester.assertEqual(att_grp_elem_back, elem)
         return
 
@@ -1161,14 +1161,14 @@ def create_sympl_realization(self, m):
             # computing a hyperbolic decomposition basis with respect
             # to the invariant bilinear form.
             # -----------------------------------------------------------
-            xbas =[bas[mhalf -i -1] for i in range(mhalf)]
-            ybas =[bas[mhalf +i]    for i in range(mhalf)]
+            xbas = [bas[mhalf - i - 1] for i in range(mhalf)]
+            ybas = [bas[mhalf + i]    for i in range(mhalf)]
 
             # -----------------------------------------------------------
             # computing the List of transvection vectors according to
             # the Assion paper, page 292.
             # -----------------------------------------------------------
-            transvections =[xbas[0]]                                   # t_1      = x_1
+            transvections = [xbas[0]]                                   # t_1      = x_1
             for i in range(mhalf-1):
                 transvections.append(ybas[i])                          # t_{2i}   = y_i
                 transvections.append(xbas[i] + xbas[i+1])              # t_{2i+1} = x_j + x_(j+1)
@@ -1234,26 +1234,26 @@ def create_unitary_realization(self, m):
             # computing a orthonormal basis with respect
             # to the invariant bilinear form.
             # -----------------------------------------------------------
-            xbas =[]
+            xbas = []
             for i in range(m):
                 if 2*i == m-1:
                     xbas.append(bas[i])
                 else:
-                    xbas.append(a*bas[i] + a.frobenius()*bas[m-1 -i])
+                    xbas.append(a*bas[i] + a.frobenius()*bas[m-1 - i])
 
             # -----------------------------------------------------------
             # computing the List of transvection vectors according to
             # Assion paper, page 293.
             # -----------------------------------------------------------
-            transvections =[xbas[0]]                                          # t_1 = x_1
+            transvections = [xbas[0]]                                          # t_1 = x_1
             if m > 1:
                 transvections.append(xbas[0]+xbas[1]+xbas[2])                 # t_2 = x_1 + x_2 + x_3
             for j in range(mthird):
                 pos = 3*(j+1)-1
                 transvections.append(xbas[pos-1])                             # t_{3i}   = x_{3i-1}
-                if pos +1  < m:
+                if pos + 1  < m:
                     transvections.append(xbas[pos-1]+xbas[pos]+xbas[pos+1])   # t_{3i+1} = x_{3i-1} + x_{3i} + x_{3i+1}
-                if pos +3  < m:
+                if pos + 3  < m:
                     transvections.append(xbas[pos+1]+xbas[pos+2]+xbas[pos+3]) # t_{3i+2} = x_{3i+1} + x_{3i+2} + x_{3i+3}
 
             # -----------------------------------------------------------
@@ -1264,7 +1264,7 @@ def create_unitary_realization(self, m):
 
             def transvec2mat(v, bas=bas, bform=bform, fact=a):
                 # note x does not change under conjugation, since it belongs to standard basis
-                t = [x + fact *(x * bform * v.conjugate()) * v for x in bas]
+                t = [x + fact * (x * bform * v.conjugate()) * v for x in bas]
                 return matrix(F, t)
 
             # ------------------------------------------------------------------------------

src/sage/groups/finitely_presented.py

@@ -643,7 +643,7 @@ def rules(self):
                 bfg = self._monoid_isomorphism.PreImagesRepresentative(bfpmon)
                 btz = bfg.UnderlyingElement().TietzeWordAbstractWord(self._free_group.gap().GeneratorsOfGroup())
                 bf = self._free_group(btz.sage())
-                dic[af]=bf
+                dic[af] = bf
         return dic
 
     def is_confluent(self):
@@ -826,7 +826,7 @@ def _repr_(self):
         """
         gens = ', '.join(self.variable_names())
         rels = ', '.join([ str(r) for r in self.relations() ])
-        return 'Finitely presented group ' + '< '+ gens + ' | ' + rels + ' >'
+        return 'Finitely presented group ' + '< ' + gens + ' | ' + rels + ' >'
 
     def _latex_(self):
         """
@@ -1112,7 +1112,7 @@ def direct_product(self, H, reduced=False, new_names=True):
             name_itr = _lexi_gen() # Python generator for lexicographical variable names
             gen_names = [next(name_itr) for i in GAP_gens]
         else:
-            gen_names= [str(g) for g in self.gens()] + [str(g) for g in H.gens()]
+            gen_names = [str(g) for g in self.gens()] + [str(g) for g in H.gens()]
         # Build the direct product in Sage for better variable names
         ret_F = FreeGroup(gen_names)
         ret_rls = tuple([ret_F(rel_word.TietzeWordAbstractWord(GAP_gens).sage())
@@ -1313,10 +1313,10 @@ def _element_constructor_(self, *args, **kwds):
             sage: H([1, 2, 1, -2]) # indirect doctest
             a*b*a*b^-1
         """
-        if len(args)!=1:
+        if len(args) != 1:
             return self.element_class(self, *args, **kwds)
         x = args[0]
-        if x==1:
+        if x == 1:
             return self.one()
         try:
             P = x.parent()

src/sage/groups/finitely_presented_named.py

@@ -196,7 +196,7 @@ def FinitelyGeneratedAbelianPresentation(int_list):
     invariants = FGP_Module(ZZ**(len(int_list)), col_sp).invariants()
     name_gen = _lexi_gen()
     F = FreeGroup([next(name_gen) for i in invariants])
-    ret_rls = [F([i+1])**invariants[i] for i in range(len(invariants)) if invariants[i]!=0]
+    ret_rls = [F([i+1])**invariants[i] for i in range(len(invariants)) if invariants[i] != 0]
 
     # Build commutator relations
     gen_pairs = [[F.gen(i),F.gen(j)] for i in range(F.ngens()-1) for j in range(i+1,F.ngens())]
@@ -285,7 +285,7 @@ def commutator(a, b):
     # Third set of relations: [z, yi] = 1
     r3 = [commutator(z, y[i]) for i in range(n)]
     # Fourth set of relations: [xi, yi] = 1 for i != j
-    r4 = [commutator(x[i], y[j]) for i in range(n) for j in range(n) if i!=j]
+    r4 = [commutator(x[i], y[j]) for i in range(n) for j in range(n) if i != j]
     rls = r1 + r2 + r3 + r4
 
     from sage.sets.primes import Primes

src/sage/groups/fqf_orthogonal.py

@@ -377,7 +377,7 @@ def _repr_(self):
             [  0 2/3]
             generated by 2 elements
         """
-        return "Group of isometries of \n%s\ngenerated by %s elements"%(self.invariant_form(), len(self.gens()))
+        return "Group of isometries of \n%s\ngenerated by %s elements" % (self.invariant_form(), len(self.gens()))
 
 class ActionOnFqf(Action):
     r"""
@@ -544,7 +544,7 @@ def orbits(G, L):
         raise ValueError("torsion quadratic modules are not isometric")
     n = len(A.smith_form_gens())
     # separating the different primes here would speed things up
-    b_cand = [[b for b in B if b.q()==a.q() and b.order() == a.order()] for a in A.smith_form_gens()]
+    b_cand = [[b for b in B if b.q() == a.q() and b.order() == a.order()] for a in A.smith_form_gens()]
 
     G = B.orthogonal_group(tuple())
     ambient = G.ambient()
@@ -566,7 +566,7 @@ def orbits(G, L):
         a = A.smith_form_gens()[i]
         card = ZZ.prod(A.smith_form_gen(k).order() for k in range(i+1))
         for b in b_cand[i]:
-            if all(b.b(f[k])==a.b(A.smith_form_gens()[k]) for k in range(i)):
+            if all(b.b(f[k]) == a.b(A.smith_form_gens()[k]) for k in range(i)):
                 fnew = f + [b]
                 # check that the elements of fnew are independent
                 if B.submodule(fnew).cardinality() == card:

src/sage/groups/free_group.py

@@ -213,20 +213,20 @@ def __init__(self, parent, x):
                 l = x.Tietze()
             except AttributeError:
                 l = list(x)
-            if len(l)>0:
+            if len(l) > 0:
                 if min(l) < -parent.ngens() or parent.ngens() < max(l):
                     raise ValueError('generators not in the group')
             if 0 in l:
                 raise ValueError('zero does not denote a generator')
-            i=0
-            while i<len(l)-1:
-                if l[i]==-l[i+1]:
+            i = 0
+            while i < len(l)-1:
+                if l[i] == -l[i+1]:
                     l.pop(i)
                     l.pop(i)
-                    if i>0:
-                        i=i-1
+                    if i > 0:
+                        i = i-1
                 else:
-                    i=i+1
+                    i = i+1
             AbstractWordTietzeWord = libgap.eval('AbstractWordTietzeWord')
             x = AbstractWordTietzeWord(l, parent.gap().GeneratorsOfGroup())
         ElementLibGAP.__init__(self, parent, x)
@@ -788,7 +788,7 @@ def _repr_(self):
             sage: G._repr_()
             'Free Group on generators {a, b}'
         """
-        return 'Free Group on generators {'+ ', '.join(self.variable_names()) + '}'
+        return 'Free Group on generators {' + ', '.join(self.variable_names()) + '}'
 
     def rank(self):
         """
@@ -870,10 +870,10 @@ def _element_constructor_(self, *args, **kwds):
             ...
             TypeError: 'sage.rings.integer.Integer' object is not iterable
         """
-        if len(args)!=1:
+        if len(args) != 1:
             return self.element_class(self, *args, **kwds)
         x = args[0]
-        if x==1 or x == [] or x == ():
+        if x == 1 or x == [] or x == ():
             return self.one()
         try:
             P = x.parent()
@@ -885,7 +885,7 @@ def _element_constructor_(self, *args, **kwds):
                 return self([i.sign()*(self._names.index(P._names[abs(i)-1])+1)
                              for i in x.Tietze()])
             else:
-                raise ValueError('generators of %s not in the group'%x)
+                raise ValueError('generators of %s not in the group' % x)
         return self.element_class(self, x, **kwds)
 
     def abelian_invariants(self):

src/sage/groups/libgap_morphism.py

@@ -546,9 +546,9 @@ def preimage(self, S):
         phi = self.gap()
         from sage.groups.perm_gps.permgroup import PermutationGroup_generic
         if not isinstance(S, (ParentLibGAP, PermutationGroup_generic)):
-            raise TypeError("%s must be a GAP or permutation group of %s"%(S, self))
+            raise TypeError("%s must be a GAP or permutation group of %s" % (S, self))
         if not self.codomain().gap().IsSubgroup(S.gap()).sage():
-            raise ValueError("%s must be a subgroup of %s"%(S, self))
+            raise ValueError("%s must be a subgroup of %s" % (S, self))
         preimage = phi.PreImage(S.gap())
         return self.domain()._subgroup_constructor(preimage)
 

src/sage/interfaces/axiom.py

@@ -275,7 +275,7 @@ def _read_in_file_command(self, filename):
         # For some reason this trivial comp
         # keeps certain random freezes from occurring.  Do not remove this.
         # The space before the \n is also important.
-        return ')read %s \n'%filename
+        return ')read %s \n' % filename
 
     def _quit_string(self):
         """
@@ -384,11 +384,11 @@ def set(self, var, value):
             '2'
 
         """
-        cmd = '%s := %s'%(var, value)
+        cmd = '%s := %s' % (var, value)
         out = self._eval_line(cmd, reformat=False)
 
         if out.find("error") != -1:
-            raise TypeError("Error executing code in Axiom\nCODE:\n\t%s\nAxiom ERROR:\n\t%s"%(cmd, out))
+            raise TypeError("Error executing code in Axiom\nCODE:\n\t%s\nAxiom ERROR:\n\t%s" % (cmd, out))
 
     def get(self, var):
         r"""
@@ -565,7 +565,7 @@ def __call__(self, x):
         """
         self._check_valid()
         P = self.parent()
-        return P('%s(%s)'%(self.name(), x))
+        return P('%s(%s)' % (self.name(), x))
 
     def _richcmp_(self, other, op):
         """
@@ -601,11 +601,11 @@ def _richcmp_(self, other, op):
 
         """
         P = self.parent()
-        if 'true' in P.eval("(%s = %s) :: Boolean"%(self.name(),other.name())):
+        if 'true' in P.eval("(%s = %s) :: Boolean" % (self.name(),other.name())):
             return rich_to_bool(op, 0)
-        elif 'true' in P.eval("(%s < %s) :: Boolean"%(self.name(), other.name())):
+        elif 'true' in P.eval("(%s < %s) :: Boolean" % (self.name(), other.name())):
             return rich_to_bool(op, -1)
-        elif 'true' in P.eval("(%s > %s) :: Boolean"%(self.name(),other.name())):
+        elif 'true' in P.eval("(%s > %s) :: Boolean" % (self.name(),other.name())):
             return rich_to_bool(op, 1)
 
         return NotImplemented
@@ -635,7 +635,7 @@ def __len__(self):
             6
         """
         P = self._check_valid()
-        s = P.eval('# %s '%self.name())
+        s = P.eval('# %s ' % self.name())
         i = s.rfind('Type')
         return int(s[:i-1])
 
@@ -667,9 +667,9 @@ def __getitem__(self, n):
             raise IndexError("index out of range")
         P = self._check_valid()
         if not isinstance(n, tuple):
-            return P.new('%s(%s)'%(self._name, n))
+            return P.new('%s(%s)' % (self._name, n))
         else:
-            return P.new('%s(%s)'%(self._name, str(n)[1:-1]))
+            return P.new('%s(%s)' % (self._name, str(n)[1:-1]))
 
     def comma(self, *args):
         """
@@ -733,7 +733,7 @@ def as_type(self, type):
         """
         P = self._check_valid()
         type = P(type)
-        return P.new("%s :: %s"%(self.name(), type.name()))
+        return P.new("%s :: %s" % (self.name(), type.name()))
 
     def unparsed_input_form(self):
         """
@@ -750,7 +750,7 @@ def unparsed_input_form(self):
 
         """
         P = self._check_valid()
-        s = P.eval('unparse(%s::InputForm)'%self._name)
+        s = P.eval('unparse(%s::InputForm)' % self._name)
         if 'translation error' in s or 'Cannot convert' in s:
             raise NotImplementedError
         s = multiple_replace({'\r\n':'', # fix stupid Fortran-ish
@@ -855,7 +855,7 @@ def _sage_(self):
          #If all else fails, try using the unparsed input form
         try:
             import sage.misc.sage_eval
-            vars=sage.symbolic.ring.var(str(self.variables())[1:-1])
+            vars = sage.symbolic.ring.var(str(self.variables())[1:-1])
             if isinstance(vars,tuple):
                 return sage.misc.sage_eval.sage_eval(self.unparsed_input_form(), locals={str(x):x for x in vars})
             else:

src/sage/interfaces/four_ti_2.py

@@ -176,7 +176,7 @@ def write_array(self, array, nrows, ncols, filename):
             sage: four_ti_2.write_array([[1,2,3],[3,4,5]], 2, 3, "test_file")
         """
         f = open(os.path.join(self.directory(), filename), 'w')
-        f.write("%s %s\n"%(nrows, ncols))
+        f.write("%s %s\n" % (nrows, ncols))
         for row in array:
             f.write(" ".join(map(str, row)))
             f.write("\n")
@@ -444,7 +444,7 @@ def ppi(self, n):
 
         """
         self.call('ppi', f'{n} 2> /dev/null')
-        return self.read_matrix('ppi%s.gra'%n)
+        return self.read_matrix('ppi%s.gra' % n)
 
     def circuits(self, mat=None, project=None):
         r"""

src/sage/interfaces/frobby.py

@@ -168,14 +168,14 @@ def hilbert(self, monomial_ideal):
         """
         frobby_input = self._ideal_to_string(monomial_ideal)
         frobby_output = self('hilbert', input=frobby_input)
-        ring=monomial_ideal.ring()
-        lines=frobby_output.split('\n')
-        if lines[-1]=='':
+        ring = monomial_ideal.ring()
+        lines = frobby_output.split('\n')
+        if lines[-1] == '':
             lines.pop(-1)
-        if lines[-1]=='(coefficient)':
+        if lines[-1] == '(coefficient)':
             lines.pop(-1)
         lines.pop(0)
-        resul=0
+        resul = 0
         for l in lines:
             lis = [int(_) for _ in l.split()]
             resul += lis[0]+prod([ring.gen(i)**lis[i+1] for i in range(len(lis)-1)])
@@ -206,9 +206,9 @@ def associated_primes(self, monomial_ideal):
         """
         frobby_input = self._ideal_to_string(monomial_ideal)
         frobby_output = self('assoprimes', input=frobby_input)
-        lines=frobby_output.split('\n')
+        lines = frobby_output.split('\n')
         lines.pop(0)
-        if lines[-1]=='':
+        if lines[-1] == '':
             lines.pop(-1)
         lists = [[int(_) for _ in a.split()] for a in lines]
 
@@ -334,10 +334,10 @@ def _parse_ideals(self, string, ring):
                 lines.pop(0)
                 matrices.append('1 '+str(ring.ngens())+'\n'+'0 '*ring.ngens()+'\n')
             else:
-                nrows=int(lines[0].split()[0])
-                nmatrix=lines.pop(0)+'\n'
+                nrows = int(lines[0].split()[0])
+                nmatrix = lines.pop(0)+'\n'
                 for i in range(nrows):
-                    nmatrix+=lines.pop(0)+'\n'
+                    nmatrix += lines.pop(0)+'\n'
                 matrices.append(nmatrix)
 
         def to_ideal(exps):